Question

The molar specific heat of an ideal gas at constant pressure and constant volume is $'C_p'$ and $'C_v'$ respectively. If 'R' is the universal gas constant and the ratio of $'C_p'$ to $'C_v'$ is $'\gamma'$ then $C_v =$

• A. $\frac{1 - \gamma}{1 + \gamma}$
• B. $\frac{1 + \gamma}{1 - \gamma}$
• C. $\frac{ \gamma - 1 }{R}$
• D. $\frac{R}{ \gamma - 1 }$

Answer 1

Answer: (D)

According to Mayer formula,
$C_{p}-C_{V}=R \,\, \dots$(i)
where, $C_{p}=$ specific heat at constant pressure,
$C_{V}=$ specific heat at constant volume
and $\,\,\,\, R=$ gas constant
Now,$\,\,\,\,\,\gamma=\frac{C_{p}}{C_{V}}$
$\Rightarrow \,\,\,\, C_{p}=\gamma G_{V} \,\,\,\,\,\, ...(ii)$
From Eqs. (i) and (ii), we get
$\Rightarrow \,\,\,\,\, \gamma C_{V}-C_{V}=R \Rightarrow C_{V}(\gamma-1)=R$
$\Rightarrow \,\,\,\, C_{V}=\frac{R}{(\gamma-1)}$